Infrared and mass regularization in AF field theories ; 1, phi$^{3}_{6}$

In the framework of asymptotically free (AF) field theories the authors determine the correction terms in the renormalization group (RG) approach to deep inelastic (DI) scattering and to the Drell-Yan (DY) process. This leads us to an order g/sup 2/ analysis of the DI/DY parton cross sections. Some of their contributions reveal ultraviolet (UV), infrared (IR) and mass (M) divergences which, after regularization, are removed by renormalization, IR and (partially) M cancellation. The initial-state M divergences, persisting in both processes, are removed by M factorization. Consistent IR and M regularization is constrained by the double-cut rule: its meaning and implications are explained. The calculations are performed in phi /sub 6//sup 3/ theory which is AF, IR finite and technically simple. They use 'on-shell', 'off-shell' and 'massless' (n-dimensional) mass assignments and demonstrate explicitly the regularization independence of the correction term. (10 refs).